Question

if m∠wyx = m∠wyz = 45°, wx = u + 46, and wz = 3u, what is the value of u? diagram shows points w, y, z, x with right angles at z and x, and segments wz, wx, wy, yz, yx

Explanation:

Step1: Identify congruent segments

Since \( m\angle WYX = m\angle WYZ = 45^\circ \) and \( WZ \perp YZ \), \( WX \perp YX \), by the Angle - Bisector Theorem (or the property of angle - bisector and perpendiculars), \( WX = WZ \).

Step2: Set up the equation

We know that \( WX = u + 46 \) and \( WZ = 3u \). Since \( WX = WZ \), we can set up the equation:
\( u + 46=3u \)

Step3: Solve for \( u \)

Subtract \( u \) from both sides of the equation:
\( 46 = 3u - u \)
\( 46 = 2u \)
Then divide both sides by 2:
\( u=\frac{46}{2}=23 \)

Answer:

\( 23 \)